Positive Energy Levels Research Articles

The effects of leadership and autonomy on vitality: Evidence from a survey and an experiment

Employees who show high vitality at work have a high level of activation and positive energy, and often have higher job performance than their less vital colleagues. However, few studies within public administration examine vitality, looking more often at for instance job satisfaction or commitment. This study analyzes how two important work characteristics (leadership communication and autonomy) influence employee vitality. A multi-method design was used: a survey of 1,502 public healthcare employees and a lab experiment of 102 participants. Hence, this study answers to calls within public administration for 1) more multi-method designs and 2) increased use of experiments. In the survey and the experiment, both leadership communication and work autonomy have a positive effect on vitality (significant direct effects). The interaction effect of leadership communication and autonomy was weak (survey) or insignificant (lab experiment). Concluding, employee vitality can be strengthened by increased leadership communication and granting more autonomy to employees.

The 3-dimensional cored and logarithm potentials: Periodic orbits

We study analytically families of periodic orbits for the cored and logarithmic Hamiltonians with 3 degrees of freedom, which are relevant in the analysis of the galactic dynamics. First, after introducing a scale transformation in the coordinates and momenta with a parameter ɛ, we show that both systems give essentially the same set of equations of motion up to first order in ɛ. Then the conditions for finding families of periodic orbits, using the averaging theory up to first order in ɛ, apply equally to both systems in every energy level H = h > 0 showing the existence of at least 3 periodic orbits, for ɛ small enough, and also provides an analytic approximation for the initial conditions of these periodic orbits. We prove that at every positive energy level the cored and logarithmic Hamiltonians with 3 degrees of freedom have at least three periodic solutions. The technique used for proving such a result can be applied to other Hamiltonian systems.

Existence and symmetry of positive ground states for a doubly critical Schrödinger system

We study the following doubly critical Schrödinger system: \[ { − Δ u − λ 1 | x | 2 u = u 2 ∗ − 1 + ν α u α − 1 v β , x ∈ R N , − Δ v − λ 2 | x | 2 v = v 2 ∗ − 1 + ν β u α v β − 1 , x ∈ R N , u , v ∈ D 1 , 2 ( R N ) , u , v > 0 in R N ∖ { 0 } , \begin {cases}-\Delta u -\frac {\lambda _1}{|x|^2}u=u^{2^\ast -1}+ \nu \alpha u^{\alpha -1}v^\beta , \quad x\in \mathbb {R}^N,\\ -\Delta v -\frac {\lambda _2}{|x|^2}v=v^{2^\ast -1} + \nu \beta u^{\alpha }v^{\beta -1}, \quad x\in \mathbb {R}^N,\\ u,\, v\in D^{1, 2}(\mathbb {R}^N),\quad u,\, v>0\,\,\hbox {in $\mathbb {R}^N\setminus \{0\}$},\end {cases} \] where N ≥ 3 N\ge 3 , λ 1 , λ 2 ∈ ( 0 , ( N − 2 ) 2 4 ) \lambda _1, \lambda _2\in (0, \frac {(N-2)^2}{4}) , 2 ∗ = 2 N N − 2 2^\ast =\frac {2N}{N-2} and α > 1 , β > 1 \alpha >1, \beta >1 satisfying α + β = 2 ∗ \alpha +\beta =2^\ast . This problem is related to coupled nonlinear Schrödinger equations with critical exponent for Bose-Einstein condensate. For different ranges of N N , α \alpha , β \beta and ν > 0 \nu >0 , we obtain positive ground state solutions via some quite different variational methods, which are all radially symmetric. It turns out that the least energy level depends heavily on the relations among α , β \alpha , \,\beta and 2 2 . Besides, for sufficiently small ν > 0 \nu >0 , positive solutions are also obtained via a variational perturbation approach. Note that the Palais-Smale condition cannot hold for any positive energy level, which makes the study via variational methods rather complicated.

Quantum nonthermal radiation of nonstationary rotating de Sitter cosmological model

Using the Hamilton–Jacobi method a study of quantum nonthermal radiation of nonstationary rotating de Sitter cosmological model is carried out. It is shown that there exist seas of positive and negative energy states in the vicinity of the cosmological event horizon and there also exists a forbidden energy gap between the two seas. The forbidden energy gap vanishes on the surface of the cosmological event horizon so that the positive and negative energy levels overlap. The width of the forbidden energy gap and the energy of the particle at the cosmological event horizon are found to depend on the cosmological constant, the rotation parameter, positions of the particle and the cosmological event horizon, angular momentum of the particle, evaporation rate and shape of the cosmological event horizon. The tunneling probability of the emitted particles constituting Hawking radiation is also deduced for stationary nonrotating de Sitter cosmological model and the standard Hawking temperature is recovered.

Cyclometalated sensitizers for DSSCs employing cobalt redox shuttles

Two novel thiocyanate-free heteroleptic ruthenium (II) cyclometalated complexes with long chain hydrophobic groups, [Ru(ppy)(dnbpy)(dcbpy)](PF6) (ss-14) and [Ru(dFppy)(dnbpy)(dcbpy)](PF6) (ss-22) (dnbpy=4,4′-dinonyl-2,2′-bipyridine; dcbpy=2,2′-bipyridine-4,4′-dicarboxylic acid; ppy=2-phenylpyridine; dFppy=2-(2,4-difluorophenyl)pyridine) were synthesized, characterized and applied in dye sensitized solar cells (DSSC) using the [Co(dmbpy)3]2+/3+ (dmbpy=4,4′-dimethyl-2,2′-bipyridine) redox shuttle. The optical and electrochemical properties were compared to that of benchmark DSSC dye Z907 and a previously reported parent cyclometalated complex [Ru(ppy)(bpy)(dcbpy)](PF6) (1d). Functionalization of the bpy ligand with dinonyl groups combined with the addition of electron withdrawing fluorine substituents on the 2-phenylpyridine ligand resulted in enhanced light absorption and longer electron lifetimes compared to 1d, and a sufficiently positive HOMO energy level for regeneration. As a consequence of such sensitizer engineering, an overall power conversion efficiency in excess of 3% with [Co(dmbpy)3]2+/3+ was achieved.

超导态零电阻特性形成条件和相图解释

自从1986年发现高温超导体以来，令人兴奋也存在困惑，过去非常成功的超导理论却不能全面解释相图。为探索解释相图，从超导态零电阻特性入手，以超导电子配对机制为线索，抓住零电阻状态必定存在没有电场的通路，也就是在通路内电场强度处处为零；根据光电效应或者量子隧穿现象，当电子逸出后必定留下空穴，并且这些空穴一定在每一个原子核周围形成空穴电场，因而使每一个原子核周围可以出现合电场强度等于零的空间区域。应用静电场高斯定理，求出了核外合电场强度，找到了合电场强度等于零的条件。当相邻原子之间合电场强度等于零的球面相切或相交时，便形成了整块材料内零场强的通路，出现超导态零电阻特性。依据零场强通路的条件解释了令人困惑的p型和n型材料高温超导相图及多超导态。以核外电子在合电场中受力，建立了合力运动方程，求出了能量解，当空穴数量满足解中电子的电位能大于零时，电子具有正能级，而非负能级，电子从正能级激发到零能级便产生了赝能隙。根据超导电子配对机制和零场强通路的条件，提出了室温超导材料的研制方向。 Since the high-temperature superconductivity had been discovered in 1986, people are being excited, but they are being bemused, because the successful theory of superconductivity in the past could not fully explain the superconductivity phase diagrams. Therefore, revealing the physical mechanism and developing room temperature superconducting materials have become an important orientation of scientists. In order to explore the interpretation of phase diagram, it is to begin from the zero-resistance of the superconducting state, to hold this main point that the appearing zero-resistance necessarily exists in a thoroughfare of no electrostatic field, or electrostatic field intensity everywhere equals zero in the thoroughfare; according to photoelectric effect or quantum tunneling, after any electron being emitted, a hole carrier is left necessarily, and it generates electrostatic field of the hole carrier around every atomic nucleus, thus a spherical surface that vector sum of electrostatic field intensity equals zero can appear around every atomic nucleus. To apply the Gauss theorem of electrostatic field, the expression of vector sum of electrostatic field intensity and vector sum to zero equaling qualifications have been derived. When the spherical surfaces of adjacent atoms with zero sum-vector are tangent or intersecting, no electrostatic field thoroughfare is formed within the whole piece of material, and the zero-resistance characteristics of the superconducting state are showed. Qualifications of the no electrostatic field, thoroughfare can explain the bemusement about the high-temperature phase diagram and the multi-superconducting state of the p-type and n-type materials. According to the force for a electron in the sum of electrostatic field, the motion equations of the composite force is established, then the energy solution is found. When hole carrier number is satisfied to that the electronic potential energy is bigger than zero in the solution, the electron has a positive energy level, but has not a normal minus energy level. When the electron has been moved from the positive energy level to the zero energy level, the pseudogap has been generated. According to qualifications of the no electrostatic field thoroughfare, a way to explore the room-temperature superconducting materials has been proposed.

Periodic Solutions, Stability and Non-Integrability in a Generalized Hénon-Heiles Hamiltonian System

We consider the Hamiltonian function defined by the cubic polynomial , where A, B, D ∈ ℝ are parameters and so H is an extension of the well known Hénon-Heiles problem. Our main contribution for D ≠ 0, A + B ≠ 0 and other technical restrictions are in three aspects: existence of periodic solutions, stability and instability of these periodic solutions and the problem of non-integrability of the system associated to H. Initially we give sufficient conditions on the three parameters of these generalized Hénon-Heiles systems, which guarantees that at any positive energy level, the Hamiltonian system has periodic orbits. After that, we prove that its stability changes with the values of the parameters. Finally, we show that the generalized Hénon–Heiles systems cannot have any second first integral of class 1 in the sense of Liouville–Arnol'd. In fact, the parameters where our problem is not integrable in the sense of Liouville–Arnol'd are the same where the periodic orbits were analytically found through averaging theory.

The quantum nonthermal radiation and horizon surface gravity of an arbitrarily accelerating black hole with electric charge and magnetic charge

Using a new tortoise coordinate transformation, we discuss the quantum nonthermal radiation characteristics near an event horizon by studying the Hamilton-Jacobi equation of a scalar particle in curved space-time, and obtain the event horizon surface gravity and the Hawking temperature on that event horizon. The results show that there is a crossing of particle energy near the event horizon. We derive the maximum overlap of the positive and negative energy levels. It is also found that the Hawking temperature of a black hole depends not only on the time, but also on the angle. There is a problem of dimension in the usual tortoise coordinate, so the present results obtained by using a correct-dimension new tortoise coordinate transformation may be more reasonable.

Infinitely many solutions for p-harmonic equation with singular term

In this paper, we study the following p-harmonic problem involving the Hardy term: where Ω is an open bounded domain containing the origin in , and . By using the variational method, we prove that the above problem has infinitely many solutions with positive energy levels. AMS Subject Classification:35J60, 35J65.

Dynamics of a galactic Hamiltonian system

We study an even polynomial potential which appears in the study of the galactic dynamics. We prove the existence of four families of periodic orbits in every positive energy level, and we compute an analytic approximation of them. Using such periodic orbits we provide information about the non-integrability of this Hamiltonian system.

Spontaneous breaking of permutation symmetry in pseudo-Hermitian quantum mechanics

By adding an imaginary interacting term proportional to $i{p}_{1}{p}_{2}$ to the Hamiltonian of a free anisotropic planar oscillator, we construct a model which is described by the $PT$-pseudo-Hermitian Hamiltonian with the permutation symmetry of two dimensions. We prove that our model is equivalent to the Pais-Uhlenbeck oscillator and thus establish a relationship between our $PT$-pseudo-Hermitian system and the fourth-order derivative oscillator model. We also point out the spontaneous breaking of permutation symmetry which plays a crucial role in giving a real spectrum free of interchange of positive and negative energy levels in our model. Moreover, we find that the permutation symmetry of two dimensions in our Hamiltonian corresponds to the identity (not in magnitude but in attribute) of two different frequencies in the Pais-Uhlenbeck oscillator, and reveal that the unequal-frequency condition imposed as a prerequisite upon the Pais-Uhlenbeck oscillator can reasonably be explained as the spontaneous breaking of this identity.

Periodic orbits and non-integrability of Hénon–Heiles systems

We apply the averaging theory of second order to study the periodic orbits for a generalized Hénon–Heiles system with two parameters, which contains the classical Hénon–Heiles system. Two main results are shown. The first result provides sufficient conditions on the two parameters of these generalized systems, which guarantee that at any positive energy level, the Hamiltonian system has periodic orbits. These periodic orbits form in the whole phase space a continuous family of periodic orbits parameterized by the energy. The second result shows that for the non-integrable Hénon–Heiles systems in the sense of Liouville–Arnol'd, which have the periodic orbits analytically found with averaging theory, cannot exist any second first integral of class . In particular, for any second first integral of class , we prove that the classical Hénon–Heiles system and many generalizations of it are not integrable in the sense of Liouville–Arnol'd. Moreover, the tools we use for studying the periodic orbits and the non-Liouville–Arnol'd integrability can be applied to Hamiltonian systems with an arbitrary number of degrees of freedom.

Hawking effect and quantum nonthermal radiation of an arbitrarily accelerating charged black hole using a new tortoise coordinate transformation

Using a new tortoise coordinate transformation, this paper investigates the Hawking effect from an arbitrarily accelerating charged black hole by the improved Damour—Ruffini method. After the tortoise coordinate transformation, the Klein—Gordon equation can be written as the standard form at the event horizon. Then extending the outgoing wave from outside to inside of the horizon analytically, the surface gravity and Hawking temperature can be obtained automatically. It is found that the Hawking temperatures of different points on the surface are different. The quantum nonthermal radiation characteristics of a black hole near the event horizon is also discussed by studying the Hamilton—Jacobi equation in curved spacetime and the maximum overlap of the positive and negative energy levels near the event horizon is given. There is a dimensional problem in the standard tortoise coordinate and the present results may be more reasonable.

Improved microscopic-macroscopic approach incorporating the effects of continuum states

The Woods-Saxon-Strutinsky method (the microscopic-macroscopic method) combined with Kruppa's prescription for positive energy levels, which is necessary to treat neutron rich nuclei, is studied to clarify the reason for its success and to propose improvements for its shortcomings. The reason why the plateau condition is met for the Nilsson model but not for the Woods-Saxon model is understood in a new interpretation of the Strutinsky smoothing procedure as a low-pass filter. Essential features of Kruppa's level density is extracted in terms of the Thomas-Fermi approximation modified to describe spectra obtained from diagonalization in truncated oscillator bases. A method is proposed which weakens the dependence on the smoothing width by applying the Strutinsky smoothing only to the deviations from a reference level density. The BCS equations are modified for the Kruppa's spectrum, which is necessary to treat the pairing correlation properly in the presence of continuum. The potential depth is adjusted for the consistency between the microscopic and macroscopic Fermi energies. It is shown, with these improvements, that the microscopic-macroscopic method is now capable to reliably calculate binding energies of nuclei far from stability.

An update on the -symmetric complexified Scarf II potential, spectral singularities and some remarks on the rationally extended supersymmetric partners

The -symmetric complexified Scarf II potential V(x) = −V1sech2x + iV2sechxtanh x, V1 > 0, V2 ≠ 0, is revisited to study the interplay among its coupling parameters. The existence of an isolated real and positive energy level that has recently been identified as a spectral singularity or zero-width resonance is here demonstrated through the behaviour of the corresponding wavefunctions and some property of the associated pseudo-norms is pointed out. We also construct four different rationally extended supersymmetric partners to V(x), which are -symmetric or complex non--symmetric according to the coupling parameters range. A detailed study of one of these partners reveals that SUSY preserves the V(x) spectral singularity existence.

Quantum cosmological Friedman models with a Yang–Mills field and positive energy levels**This work has been supported by the DFG.

We prove the existence of a spectral resolution of the Wheeler–DeWitt equation when the matter field is provided by a Yang–Mills field, with or without mass term, if the spatial geometry of the underlying spacetime is homothetic to . The energy levels of the resulting quantum model, i.e. the eigenvalues of the corresponding self-adjoint Hamiltonian with a pure point spectrum, are strictly positive.

On the distribution of integer random variables related by two linear inequalities: I

The authors’ two preceding papers deal with the problem on the allocation of indistinguishable particles to positive integer energy levels under the condition that the total energy of the system is bounded above by some constant M. The estimates proved there imply that, for large M, most of the allocations concentrate near a limit distribution (which is the Bose-Einstein distribution, provided that the particles obey the corresponding statistics). The present paper continues this trend of research by considering the case in which not only the total energy is constrained but also the overall number of particles is specified. We study both the Bose and the Gibbs distribution and analyze the phenomenon whereby the Bose distribution passes into the Gibbs distribution in the limit as the number of particles is relatively small.

The 2-body problem under Fock's potential

We study the two-body problem moving under the Fock's potential, where the global flow is fully described. The analysis is separately performed for negative, zero, and positive energy levels. Many kinds of orbits are found, some of them being of positive Lebesgue measure. We also show some unusual features as the coexistence of fundamentally different orbits for the same energy level and for the same angular momentum.

Mean-Field Theoretical Structure of He and Be Isotopes

The structures of He and Be even-even isotopes are investigated using an axially symmetric Hartree-Fock approach with a Skyrme-IIIls mean field potential. In these simple HF calculations, He and Be isotopes appear to be prolate in their ground states and Be isotopes have oblate shape isomeric states. It is also shown that there exists a level crossing when the nuclear shape changes from the prolate state to the oblate state. The single neutron levels of Be isotopes exhibit a neutron magic number 6 instead of 8 and show that the level inversion between 1/2- and 1/2+ levels occurs only for a largely deformed isotope. Protons are bound stronger in the isotope with more neutrons while neutron levels are somewhat insensitive to the number of neutrons and thus the nuclear size and also the neutron skin become larger as the neutron number increases. In these simple calculations with Skyrme-IIIls interaction no system with a clear indication of neutron halo was found among He and Be isotopes. Instead of it we have found 8He+2n, 2n+8He+2n, and 16Be+2n like chain structures with clusters of two correlated neutrons. It is also shown that 8He and 14Be in their ground states are below the neutron drip line in which all nucleons are bound with negative energy and that 16Be in its ground state is beyond the neutron drip line with two neutrons in positive energy levels.

Letter: Quantum Nonthermal Radiation of Nonstationary Kerr-Newman-de Sitter Black Holes

Quantum nonthermal radiation of a nonstationary Kerr-Newman-de Sitter black hole is investigated. A crossing of the positive and negative Dirac energy levels occurs in a region near the event horizon of the hole, and spontaneous quantum nonthermal radiation takes place in the overlap region.